Only 3 magic schools?

[uncmark]

No: HPFGUIDX 34593

In Goblet of Fire, Harry was surprised that he had never considered 
how many wizards there were worldwide. There were over 100,000 at the 
Quidditch World cup Final and those tickets were 
considered 'impossible to get. I think we could reasonably estimate 
the worldwidw wizard population at 1 million (which would place 1 
wizard in every 5000 to 6000 births)

Are we further to guess from the Triwizard Tournament that there are 
only 3 secondary schools worldwide? They represent the UK. France, 
and the Eastern European groups, but conspicuously missing are 
Americans, Orientals, Africans, or Latinos. Do these populations have 
no magical schools?

I think that Hogwarts, Durmstrang, and Beauxbaton might be the three 
oldest only, much like the US 'ivy league'. It was mentioned that the 
Tournament hadn't been held in centuries. There are probably schools 
in other regions, maybe we'll see them in later books. 

Thoughts on the subject?

Uncmark